Get three vectors to form a base

Question

Be the vector space of ${\rm I\!R}^5$ and the vectors (1, 2, 0, 2, 3) and (5, 3, 0, 3, 0) of said space:

I'm trying to get three other vectors that, together with the two previous ones, form a basis of the vector space ${\rm I\!R}^5$.

Answer 1

HINT

Let consider the matrix with the $2$ given vectors as row and row reduce, then add the $e_i$ linearly independent vectors from the standard basis.